We look at the division of 17603 by 42 
We're looking to find how many times 42 goes into 17603.

Moving on to step 1:
42 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 42

Going ahead to step 2:
When dividing 17 by 42, we get 0 with a remainder of 17.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Take the next digit (6) from the dividend and append it to 17, then repeat: 176 / 42

Going ahead to step 3:
If we divide 176 by 42, we get 4 and a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
The remainder is 8 after subtracting 168 from 176.
Fetch the next digit (0) from the dividend, attach it to 8 and continue: 80 / 42

On to step 4:
42 can be fit into 80 1 times, resulting in a remainder of 38.
Use 1 as the next digit of our solution. 
Result so far: 41.0
If we subtract 42 from 80, we get 38.
Grab the next digit (3) from the dividend, add it to 38, then carry on: 383 / 42

Let's proceed to step 5:
If we divide 383 by 42, we get 9 and a remainder of 5.
Put 9 as the next digit of the answer. 
Result so far: 419.0
If we subtract 378 from 383, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 6:
50 divided by 42 is 1 with a remainder of 8.
The next digit of our result is 1. 
Result so far: 419.1
Deduct 42 from 50 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
The number 42 fits into 80 1 times, leaving a remainder of 38.
Use 1 as the next digit of our solution. 
Result so far: 419.11
If we subtract 42 from 80, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The quotient of the division is 419.11, and the remainder is 0.038.